Final answer:
The rule that represents the total charge, y, for x hours of service by the landscaper is y = 35 + 50x. This equation includes a fixed charge of $35 and an hourly rate of $50.
Step-by-step explanation:
The landscaper's total charge, y, for x hours of service can be represented by a linear equation. To write the rule, we consider the fixed cost and the hourly charge. The landscaper charges a fixed cost or starting fee which is constant for any service, and this is $35. Then there is an additional variable cost of $50 for every hour of service. Hence, the total charge will be the sum of the fixed cost and the variable cost based on the number of hours worked.
Therefore, the equation representing the total charge would be y = 35 + 50x.
Here, x represents the independent variable, which is the number of hours of service, and y represents the dependent variable, which is the total charge. The y-intercept in this case is 35, and the slope is 50, implying that for each additional hour of service, the total charge increases by $50.
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